Question

a triangular pyramid has these dimensions. the sides of the base are 3 centimeters, 4 centimeters, and 5 centimeters. the height is 7 centimeters. what is the volume of the pyramid? 1 of 4 questio 84 cm³ 14 cm³ 28 cm³ 42 cm³

Explanation:

Step1: Determine the base area

Since the base sides are \(3\), \(4\), \(5\) (a right - triangle as \(3^{2}+4^{2}=5^{2}\)), the area of the base \(B=\frac{1}{2}\times3\times4\).

$$B = 6\space cm^{2}$$

Step2: Calculate the volume

The volume formula for a pyramid is \(V=\frac{1}{3}Bh\), where \(h = 7\space cm\) and \(B = 6\space cm^{2}\).

$$V=\frac{1}{3}\times6\times7$$

$$V = 14\space cm^{3}$$

Answer:

\(14\space cm^{3}\) (the second option)